Question: Simplify the following expression: $ a = \dfrac{-3n - 7}{-8} + \dfrac{-8}{3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-3n - 7}{-8} \times \dfrac{3}{3} = \dfrac{-9n - 21}{-24} $ Multiply the second expression by $\dfrac{-8}{-8}$ $ \dfrac{-8}{3} \times \dfrac{-8}{-8} = \dfrac{64}{-24} $ Therefore $ a = \dfrac{-9n - 21}{-24} + \dfrac{64}{-24} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-9n - 21 + 64}{-24} $ $a = \dfrac{-9n + 43}{-24}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{9n - 43}{24}$